Questions: Solve for (x) (z=2x-3y)

Solve for (x)
(z=2x-3y)
Transcript text: Solve for $x$ \[ z=2 x-3 y \]
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Solution

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Solution Steps

To solve for x x in the equation z=2x3y z = 2x - 3y , we need to isolate x x on one side of the equation. This involves rearranging the equation by performing algebraic operations.

Solution Approach
  1. Add 3y 3y to both sides of the equation to move the y y -term to the left side.
  2. Divide both sides by 2 to solve for x x .
Step 1: Add 3y 3y to both sides

Starting with the equation: z=2x3y z = 2x - 3y we add 3y 3y to both sides to isolate the term with x x : z+3y=2x z + 3y = 2x

Step 2: Divide both sides by 2

Next, we divide both sides of the equation by 2 to solve for x x : x=z+3y2 x = \frac{z + 3y}{2}

Step 3: Substitute the given values

Given z=10 z = 10 and y=2 y = 2 , we substitute these values into the equation: x=10+322 x = \frac{10 + 3 \cdot 2}{2}

Step 4: Simplify the expression

Simplify the expression to find the value of x x : x=10+62=162=8.0 x = \frac{10 + 6}{2} = \frac{16}{2} = 8.0

Final Answer

x=z+3y2 \boxed{x = \frac{z + 3y}{2}}

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